Finite Group Databasebeta

← #29685870

Subgroups — #29685870

Order 15616.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic, complemented
2#21455035C211yesmaximal, characteristic
3C2×#16839882C211yesmaximal, characteristic, complemented
4C2×#16839877C211yesmaximal, characteristic, complemented
5#21446149C211yesmaximal, characteristic, complemented
6#21446149C211yesmaximal, characteristic, complemented
7#21446122C211yesmaximal, characteristic, complemented
8#21446093C211yesmaximal, characteristic, complemented
9#21446093C211yesmaximal, characteristic, complemented
10#21446023C211yesmaximal, characteristic, complemented
11#21445762C211yesmaximal, characteristic, complemented
12#21445665C211yesmaximal, characteristic, complemented
13#21445658C211yesmaximal, characteristic, complemented
14#21445600C211yesmaximal, characteristic, complemented
15C61×#2930C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519797C2211yescharacteristic
19#16840528—24no—
20#16840528—24no—
21C2×#14519785—21no—
22C2×#14519785—21no—
23C2×#14519783C2211yescharacteristic
24C2×#14519783C2211yescharacteristic
25C2×#14519783C2211yescharacteristic
26C2×#14519783C2211yescharacteristic
27C22×#11758194C2211yescharacteristic
28C2×M16×D61—21no—
29C2×M16×D61—21no—
30#16839922C411yescharacteristic, complemented
31#16839922C411yescharacteristic, complemented
32#16839917C411yescharacteristic, complemented
33#16839912C411yescharacteristic, complemented
34#16839905C411yescharacteristic, complemented
35#16839905C411yescharacteristic, complemented
36#16839900C411yescharacteristic, complemented
37#16839895C411yescharacteristic, complemented
38#16839882—24no—
39#16839877—24no—
40C2×#14519712C2211yescharacteristic, complemented
41C2×#14519712C2211yescharacteristic, complemented
42C2×#14519704C2211yescharacteristic, complemented
43C2×#14519704C2211yescharacteristic, complemented
44C2×#14519703C2211yescharacteristic
45C2×#14519703C2211yescharacteristic
46C2×#14519703C2211yescharacteristic
47C2×#14519703C2211yescharacteristic
48#16839756C2211yescharacteristic
49#16839756C2211yescharacteristic
50C2×C22⋊#92418C2211yescharacteristic
51C2×#14519687C2211yescharacteristic, complemented
52C2×C8×Dic61C2211yescharacteristic, complemented
53C4×C22⋊Dic61C2211yescharacteristic
54#16839526C2211yescharacteristic, complemented
55#16839526C2211yescharacteristic, complemented
56#16839521C2211yescharacteristic, complemented
57#16839521C2211yescharacteristic, complemented
58#16839516C2211yescharacteristic, complemented
59#16839516C2211yescharacteristic, complemented
60C2×#131×C61C2211yescharacteristic, complemented
61C22×M16×C61C2211yescharacteristic
62C61×#525C2211yescharacteristic
63C61×#436—21no—
64C61×#436—21no—
65C61×#435—21no—
66C61×#435—21no—
67C61×#424C2211yescharacteristic, complemented
68C61×#408C2211yescharacteristic, complemented
69C61×#407C2211yescharacteristic
70C61×#405C2211yescharacteristic, complemented
71C2×#11758222—21no—
72C2×#11758222—21no—
73C2×#11758222—22no—
74C2×#11758222—22no—
75C2×#11758222—22no—
76C2×#11758222—22no—
77C2×#11758222C2×C411yescharacteristic
78C2×#11758222C2×C411yescharacteristic
79C2×#11758222C2311yescharacteristic
80C2×#11758222C2311yescharacteristic
81C22×Dic122C2×C411yescharacteristic
82C22×D244C2×C411yescharacteristic
83C22×C22⋊D61—21no—
84C22×C4×D61—21no—
85#14519797—22no—
86#14519797—22no—
87#14519797—22no—
88#14519797—22no—
89C2×#11758202C2×C411yescharacteristic
90C2×#11758202C2×C411yescharacteristic
91C2×#11758200C2×C411yescharacteristic
92C2×#11758200C2×C411yescharacteristic
93C2×#11758201C2×C411yescharacteristic
94C2×#11758201C2×C411yescharacteristic
95C2×#11758199C2×C411yescharacteristic
96C2×#11758199C2×C411yescharacteristic
97#14519785—28no—
98#14519785—28no—
99#14519783—22no—
100#14519783—22no—
101#14519783—22no—
102#14519783—22no—
103#14519783—22no—
104#14519783—22no—
105#14519783D414yescomplemented
106#14519783D414yescomplemented
107C2×#11758194—21no—
108C2×#11758194—22no—
109C2×#11758194—22no—
110C2×#11758194C2311yescharacteristic
111C2×#11758194C2311yescharacteristic
112C2×#11758189—21no—
113C2×#11758189—21no—
114C2×#11758189—21no—
115C2×#11758189—21no—
116M16×D61—28no—
117M16×D61—28no—
118C22×#92418—21no—
119C22×#92418C2311yescharacteristic
120C22×#92418C2311yescharacteristic
121C2×C8×D61—21no—
122C2×C8×D61—21no—
123C2×C8×D61—21no—
124C2×C8×D61—21no—
125C2×C22⋊Dic61—21no—
126C2×C4×Dic61C2311yescharacteristic
127C2×C4×Dic61C2311yescharacteristic
128#14519712—22no—
129#14519712—22no—
130#14519704—22no—
131#14519704—22no—
132#14519703—22no—
133#14519703—22no—
134#14519703—22no—
135#14519703—22no—
136#14519700C2×C411yescharacteristic
137#14519700C2×C411yescharacteristic
138#14519700C2×C411yescharacteristic
139#14519700C2×C411yescharacteristic
140#14519697C2×C411yescharacteristic
141#14519697C2×C411yescharacteristic
142#14519697C2×C411yescharacteristic
143#14519697C2×C411yescharacteristic
144C22⋊#92418C2×C411yescharacteristic
145C22⋊#92418C2×C411yescharacteristic
146C22⋊#92418C2×C411yescharacteristic
147C22⋊#92418C2×C411yescharacteristic
148#14519687—22no—
149C8×Dic61—22no—
150#14519684—21no—
151C2×#41×C61C2311yescharacteristic
152C23×C4×C61C2311yescharacteristic
153#131×C61—22no—
154#131×C61—22no—
155C2×M16×C61—22no—
156C2×M16×C61—22no—
157C2×M16×C61—21no—
158C2×M16×C61D411yescharacteristic
159C2×M16×C61D411yescharacteristic
160C2×M16×C61D411yescharacteristic
161C2×M16×C61D411yescharacteristic
162C2×M16×C61C2311yescharacteristic
163C2×M16×C61C2311yescharacteristic
164C22×C8×C61—21no—
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167#123×C61—21no—
168C22⋊Q8×C61C2×C411yescharacteristic
169C22⋊Q8×C61C2×C411yescharacteristic
170#121×C61C2×C411yescharacteristic
171#121×C61C2×C411yescharacteristic
172#120×C61—21no—
173C4×D4×C61—21no—
174C4×D4×C61—21no—
175#117×C61C2311yescharacteristic
176C4⋊C8×C61—21no—
177C4⋊C8×C61—21no—
178C22⋊C8×C61—21no—
179C22⋊C8×C61—21no—
180C22⋊C8×C61—21no—
181C22⋊C8×C61—21no—
182#97×C61—21no—
183C4×C8×C61—21no—
184C24×C61#4111yescharacteristic
185C23×D61—21no—
186#41×C61—21no—
187#41×C61—21no—
188#41×C61—21no—
189#41×C61—21no—
190C2×Q8×C61C22×C411yescharacteristic
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61C22×C411yescharacteristic
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61C22×C411yescharacteristic
201C22×C4×C61C22×C411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61#4111yescharacteristic
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—21no—
209C2×C22⋊D61—21no—
210C2×C22⋊D61—21no—
211C2×C22⋊D61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215#11758222—24no—
216#11758222—24no—
217#11758222—24no—
218#11758222—24no—
219#11758222—21no—
220#11758222—21no—
221#11758222—21no—
222#11758222—21no—
223#11758222—22no—
224#11758222—22no—
225#11758222—22no—
226#11758222—22no—
227#11758222C2×D412yes—
228#11758222C2×D412yes—
229#11758222#4112yes—
230#11758222#4112yes—
231C2×D244—21no—
232C2×D244—22no—
233C2×D244—22no—
234C2×D244C22×C411yescharacteristic
235C2×D244C22×C411yescharacteristic
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×Dic122—21no—
243C2×Dic122—22no—
244C2×Dic122—22no—
245C2×Dic122C22×C411yescharacteristic
246C2×Dic122C22×C411yescharacteristic
247M16×C61—22no—
248M16×C61—22no—
249M16×C61—22no—
250M16×C61—22no—
251M16×C61—21no—
252M16×C61—21no—
253M16×C61—21no—
254M16×C61—21no—
255M16×C61—42no—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—42no—
261C2×C8×C61C2×D411yescharacteristic
262C2×C8×C61C2×D411yescharacteristic
263C2×C8×C61C2×D412yes—
264C2×C8×C61C2×D412yes—
265C2×C8×C61C2×D411yescharacteristic
266C2×C8×C61C2×D411yescharacteristic
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61C22×C411yescharacteristic
270C4⋊C4×C61C22×C411yescharacteristic
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C42×C61—21no—
277C22⋊Dic61—42no—
278#11758202—22no—
279#11758202—22no—
280#11758201—22no—
281#11758201—22no—
282#11758200—22no—
283#11758200—22no—
284#11758199—22no—
285#11758199—22no—
286C4×Dic61—21no—
287C4×Dic61—21no—
288C4×Dic61—21no—
289C4×Dic61—21no—
290#11758194—24no—
291#11758194—21no—
292#11758194—21no—
293#11758194C2×D412yes—
294#11758194C2×D412yes—
295C2×#92418—24no—
296C2×#92418—21no—
297C2×#92418—21no—
298C2×#92418—21no—
299C2×#92418—21no—
300C2×#92418—21no—
301C2×#92418—21no—
302C2×#92418C22×C411yescharacteristic
303C2×#92418C22×C411yescharacteristic
304C2×#92418C22×C411yescharacteristic
305C2×#92418C22×C411yescharacteristic
306#11758189—24no—
307#11758189—24no—
308#11758189—24no—
309#11758189—24no—
310C8×D61—24no—
311C8×D61—24no—
312C8×D61—24no—
313C8×D61—24no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61C4×D411yescharacteristic
320C23×C61C4×D411yescharacteristic
321C23×C61C2×#4111yescharacteristic
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—24no—
325C22×D61—81no—
326C22×D61—81no—
327Q8×C61—21no—
328Q8×C61—21no—
329D4×C61—21no—
330D4×C61—21no—
331D4×C61—41no—
332D4×C61—41no—
333D4×C61—81no—
334D4×C61—81no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61C4×D411yescharacteristic
351C2×C4×C61C4×D411yescharacteristic
352C2×C4×C61C23×C411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C2×#4111yescharacteristic
357C2×C4×C61C2×#4111yescharacteristic
358C22⋊D61—24no—
359C22⋊D61—24no—
360C22⋊D61—22no—
361C22⋊D61—22no—
362C22⋊D61—22no—
363C22⋊D61—22no—
364C2×Dic61—24no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—22no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373D244—24no—
374D244—21no—
375D244—21no—
376D244C4×D412yes—
377D244C4×D412yes—
378C4×D61—24no—
379C4×D61—24no—
380C4×D61—22no—
381C4×D61—22no—
382C4×D61—22no—
383C4×D61—22no—
384Dic122—24no—
385Dic122—21no—
386Dic122—21no—
387Dic122C4×D412yes—
388Dic122C4×D412yes—
389C8×C61—21no—
390C8×C61—21no—
391C8×C61—41no—
392C8×C61—41no—
393C8×C61#12012yes—
394C8×C61#12012yes—
395#92418—21no—
396#92418—21no—
397#92418—21no—
398#92418—21no—
399#92418—22no—
400#92418—22no—
401#21468—611nomaximal, Sylow
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—21no—
406C22×C61—21no—
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—81no—
414C22×C61—81no—
415C22×C61C2×C4×D411yescharacteristic
416C22×C61#52511yescharacteristic
417C22×C61#52511yescharacteristic
418C2×D61—22no—
419C2×D61—22no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—41no—
423C2×D61—41no—
424C2×D61—84no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—41no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61C2×C4×D411yescharacteristic
431C4×C61C2×C4×D411yescharacteristic
432C4×C61C2×#12011yescharacteristic
433C4×C61#52511yescharacteristic
434Dic61—22no—
435Dic61—22no—
436Dic61—42no—
437Dic61—81no—
438C2×#568—611no—
439#3002—611no—
440C2×#444—611no—
441C2×#443—611no—
442#2930D6111yescharacteristic, complemented
443#1876—611no—
444#1876—611no—
445#1871—611no—
446#1866—611no—
447#1866—611no—
448#1855—611no—
449#1789—611no—
450#1765—611no—
451#1764—611no—
452#1753—611no—
453C2×C61—21no—
454C2×C61—21no—
455C2×C61—41no—
456C2×C61—41no—
457C2×C61—81no—
458C2×C61C4×#12011yescharacteristic
459C2×C61#295611yescharacteristic
460C2×C61#295711yescharacteristic
461D61—42no—
462D61—42no—
463C22×#41—611no—
464C2×#135—611no—
465C2×#135—611no—
466#568—1224no—
467#568—1224no—
468C2×#131—611no—
469C2×#131—611no—
470C2×#131—611no—
471C2×#131—611no—
472C2×#131—1221no—
473C2×#131—1221no—
474C2×#131C2×D6111yescharacteristic, complemented
475C22×M16—611no—
476C22×M16—1221no—
477C22×M16—1221no—
478C22×M16C2×D6111yescharacteristic
479#525C2×D6111yescharacteristic
480#452—611no—
481#452—611no—
482#451—611no—
483#450—611no—
484#449—611no—
485#449—611no—
486#448—611no—
487#447—611no—
488#444—1224no—
489#443—1224no—
490#436—21no—
491#436—21no—
492#435—21no—
493#435—21no—
494C2×#108—611no—
495C2×#108—611no—
496#424C2×D6111yescharacteristic, complemented
497C2×#104—611no—
498C2×#104—611no—
499C2×#104—611no—
500C2×#104—611no—
501C2×#104—611no—
502C2×#104—611no—
503#416—611no—
504#416—611no—
505#408C2×D6111yescharacteristic, complemented
506#407C2×D6111yescharacteristic
507C2×C22⋊C8—611no—
508#405C2×D6111yescharacteristic, complemented
509C2×#97—611no—
510C2×C4×C8—611no—
511C4×C22⋊C4—611no—
512#341—611no—
513#341—611no—
514#339—611no—
515#339—611no—
516#336—611no—
517#336—611no—
518C61#2146811yescharacteristic, complemented, Sylow
519C2×#41—611no—
520C2×#41—611no—
521C2×#41—611no—
522C2×#41—611no—
523C2×#41—1222no—
524C2×#41—1222no—
525C2×#41—1222no—
526C2×#41—1222no—
527C2×#41—1221no—
528C2×#41—1221no—
529C2×#41C22×D6111yescharacteristic
530C22×Q8—611no—
531C22×D4—611no—
532C22×D4—1221no—
533C23×C4—1221no—
534C23×C4C22×D6111yescharacteristic
535#135—1222no—
536#135—1222no—
537#135—1222no—
538#135—1222no—
539C2×Q16—611no—
540C2×Q16—611no—
541C2×SD16—611no—
542C2×SD16—611no—
543C2×SD16—611no—
544C2×SD16—611no—
545C2×D8—611no—
546C2×D8—611no—
547#131—22no—
548#131—22no—
549#131—614no—
550#131—614no—
551#131—1222no—
552#131—1222no—
553#131—1222no—
554#131—1222no—
555#131—1228no—
556#131—1228no—
557#131—1222no—
558#131—1222no—
559C2×M16—22no—
560C2×M16—22no—
561C2×M16—21no—
562C2×M16—611no—
563C2×M16—611no—
564C2×M16—1228no—
565C2×M16—1228no—
566C2×M16—1222no—
567C2×M16—1222no—
568C2×M16—1221no—
569C2×M16—1221no—
570C2×M16—1221no—
571C2×M16—1221no—
572C2×M16—1221no—
573C2×M16C22⋊D6111yescharacteristic
574C2×M16C22⋊D6111yescharacteristic
575C2×M16C22⋊D6111yescharacteristic
576C2×M16C22⋊D6111yescharacteristic
577C2×M16C22×D6111yescharacteristic
578C2×M16C22×D6111yescharacteristic
579C22×C8—21no—
580C22×C8—611no—
581C22×C8—611no—
582C22×C8—1221no—
583C22×C8—1221no—
584C22×C8—1221no—
585C22×C8—1221no—
586C22×C8—1221no—
587C22×C8C22×D6111yescharacteristic
588C22×C8C22×D6111yescharacteristic
589#123—21no—
590C22⋊Q8C4×D6111yescharacteristic
591C22⋊Q8C4×D6111yescharacteristic
592#121C4×D6111yescharacteristic
593#121C4×D6111yescharacteristic
594#120—21no—
595C4×D4—21no—
596C4×D4—21no—
597#117C22×D6111yescharacteristic
598C2×C22⋊C4—1221no—
599C2×C42—611no—
600C2×C42—611no—
601#108—1222no—
602#108—1222no—
603C4⋊C8—21no—
604C4⋊C8—21no—
605#104—1222no—
606#104—1222no—
607#104—1222no—
608#104—1222no—
609#104—1222no—
610#104—1222no—
611#103—611no—
612#103—611no—
613#103—611no—
614#103—611no—
615#102—611no—
616#102—611no—
617#102—611no—
618#102—611no—
619C22⋊C8—21no—
620C22⋊C8—21no—
621C22⋊C8—21no—
622C22⋊C8—21no—
623C22⋊C8—611no—
624C22⋊C8—611no—
625C22⋊C8—611no—
626C22⋊C8—611no—
627#97—21no—
628#97—1222no—
629C4×C8—21no—
630C4×C8—1222no—
631#95—1221no—
632C24—1221no—
633C24#1175822211yescharacteristic
634#41—21no—
635#41—21no—
636#41—21no—
637#41—21no—
638#41—612no—
639#41—612no—
640#41—612no—
641#41—612no—
642#41—1222no—
643#41—1222no—
644#41—1222no—
645#41—1222no—
646#41—1224no—
647#41—1224no—
648#41—1224no—
649#41—1224no—
650#41—1221no—
651#41—1221no—
652#41—1221no—
653#41—1221no—
654C2×Q8—611no—
655C2×Q8—611no—
656C2×Q8—1222no—
657C2×Q8—1222no—
658C2×Q8—1221no—
659C2×Q8C2×C4×D6111yescharacteristic
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—611no—
664C2×D4—611no—
665C2×D4—1222no—
666C2×D4—1222no—
667C2×D4—1224no—
668C2×D4—1224no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—1221no—
674C2×D4C2×C4×D6111yescharacteristic
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—1224no—
681C22×C4—1224no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4C2×C4×D6111yescharacteristic
690C22×C4C2×C4×D6111yescharacteristic
691C22×C4#1175822211yescharacteristic
692C22×C4C2×C22⋊D6111yescharacteristic
693C22×C4C2×C22⋊D6111yescharacteristic
694C22×C4C23×D6111yescharacteristic
695Q16—1222no—
696Q16—1222no—
697SD16—1222no—
698SD16—1222no—
699SD16—1222no—
700SD16—1222no—
701D8—1222no—
702D8—1222no—
703M16—22no—
704M16—22no—
705M16—22no—
706M16—22no—
707M16—21no—
708M16—21no—
709M16—21no—
710M16—21no—
711M16—42no—
712M16—612no—
713M16—612no—
714M16—1224no—
715M16—1224no—
716M16—1224no—
717M16—1221no—
718M16—1221no—
719M16—1224no—
720M16—1224no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—42no—
726C2×C8—611no—
727C2×C8—611no—
728C2×C8—611no—
729C2×C8—611no—
730C2×C8—1224no—
731C2×C8—1224no—
732C2×C8—1224no—
733C2×C8—1221no—
734C2×C8—1221no—
735C2×C8—1221no—
736C2×C8—1221no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—1224no—
740C2×C8—1224no—
741C2×C8D4×D6112yes—
742C2×C8D4×D6112yes—
743C2×C8C2×C22⋊D6111yescharacteristic
744C2×C8C2×C22⋊D6111yescharacteristic
745C2×C8C2×C22⋊D6111yescharacteristic
746C2×C8C2×C22⋊D6111yescharacteristic
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4C2×C4×D6111yescharacteristic
750C4⋊C4C2×C4×D6111yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—2442no—
757C42—21no—
758C42—1221no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—41no—
766C23—41no—
767C23—1224no—
768C23—1221no—
769C23—1221no—
770C23—4881no—
771C23—4881no—
772C23C4×C22⋊D6111yescharacteristic
773C23C4×C22⋊D6111yescharacteristic
774C23C2×#1175822211yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—612no—
778Q8—612no—
779Q8—1224no—
780Q8—1221no—
781Q8—1221no—
782D4—21no—
783D4—21no—
784D4—41no—
785D4—41no—
786D4—81no—
787D4—81no—
788D4—612no—
789D4—612no—
790D4—1224no—
791D4—1224no—
792D4—1224no—
793D4—1222no—
794D4—1222no—
795D4—1222no—
796D4—1222no—
797D4—1221no—
798D4—1221no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—1224no—
815C2×C4—1224no—
816C2×C4—1224no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4C4×C22⋊D6111yescharacteristic
830C2×C4C4×C22⋊D6111yescharacteristic
831C2×C4C22×C4×D6111yescharacteristic
832C2×C4C2×D4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C22×C22⋊D6111yescharacteristic
835C2×C4#41×D6111yescharacteristic
836C2×C4#41×D6111yescharacteristic
837C8—21no—
838C8—21no—
839C8—41no—
840C8—41no—
841C8—1221no—
842C8—1221no—
843C8—1221no—
844C8—1221no—
845C8—1222no—
846C8—1222no—
847C8#1451974512yes—
848C8#1451974512yes—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—81no—
861C22—81no—
862C22—1222no—
863C22—1222no—
864C22—4884no—
865C22—2441no—
866C22—2441no—
867C22—2441no—
868C22—2441no—
869C22C2×C4×C22⋊D6111yescharacteristic
870C22#1684027111yescharacteristic
871C22#1684027111yescharacteristic
872C4—21no—
873C4—21no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—1222no—
878C4—1222no—
879C4—4881no—
880C4—2442no—
881C4C4×D4×D6111yescharacteristic
882C4C4×D4×D6111yescharacteristic
883C4C2×#1451974511yescharacteristic
884C4#1684026911yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—81no—
890C2—2442no—
891C2—2442no—
892C2C4×#1451974511yescharacteristic
893C2#2145472611yescharacteristic
894C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2930C2
socleC22×C61C2×C4×D4
prime radical#21455035C2
cosocleC22×C4×C61C24
hypercenter#2930D61
hypocenterC61#21468
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #2930

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16840528C2semidirect
3. C2×#16839882C2semidirect
4. C2×#16839877C2semidirect
5. #21446149C2semidirect
6. #21446149C2semidirect
7. #21446122C2semidirect
8. #21446093C2semidirect
9. #21446093C2semidirect
10. #21446023C2semidirect
11. #21445762C2semidirect
12. #21445665C2semidirect
13. #21445658C2semidirect
14. #21445600C2semidirect
15. C61×#2930C2semidirect
30. #16839922C4semidirect
31. #16839922C4semidirect
32. #16839917C4semidirect
33. #16839912C4semidirect
34. #16839905C4semidirect
35. #16839905C4semidirect
36. #16839900C4semidirect
37. #16839895C4semidirect
40. C2×#14519712C22semidirect
41. C2×#14519712C22semidirect
42. C2×#14519704C22semidirect
43. C2×#14519704C22semidirect
51. C2×#14519687C22semidirect
52. C2×C8×Dic61C22semidirect
54. #16839526C22semidirect
55. #16839526C22semidirect
56. #16839521C22semidirect
57. #16839521C22semidirect
58. #16839516C22semidirect
59. #16839516C22semidirect
60. C2×#131×C61C22semidirect
67. C61×#424C22semidirect
68. C61×#408C22semidirect
70. C61×#405C22semidirect
105. #14519783D4semidirect
106. #14519783D4semidirect
442. #2930D61semidirect
474. C2×#131C2×D61semidirect
496. #424C2×D61semidirect
505. #408C2×D61semidirect
508. #405C2×D61semidirect
518. C61#21468semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168405282
#214550352
C2×#168398822
C2×#168398772
#214461492
#214461222
#214460932
#214460232
#214457622
#214456652
#214456582
#214456002
C61×#29302
#2146861